# What is an equation in standard form of an ellipse centered at the origin with vertex (-6, 0) and covertex (0, 4)?

**Solution:**

An ellipse is the locus of points in a plane, the sum of whose distances from two fixed points is a constant value. The two fixed points are called the foci of the ellipse.

The standard equation of an ellipse is (x - h)^{2}/(a^{2}) + (y - k)^{2}/(b^{2}) = 1

Where, a is the vertex

b is the co-vertex

Given, ellipse is centred at origin

Thus, (h, k) = (0, 0)

Vertex = (-6, 0)

So, the length of a is -6.

Co-vertex = (0, 4)

So, the length of b is 4.

Now, the equation of the ellipse will be

(x - 0)^{2}/(-6)^{2} + (y - 0)^{2}/(4)² = 1

x^{2}/36 + y^{2}/16 = 1

Therefore, the equation of the ellipse is x^{2}/36 + y^{2}/16 = 1.

## What is an equation in the standard form of an ellipse centered at the origin with vertex (-6, 0) and covertex (0, 4)?

**Summary:**

An equation in standard form of an ellipse centered at the origin with vertex (-6, 0) is x^{2}/36 + y^{2}/16 = 1.

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